名校
解题方法
1 . 设
,已知函数
.
(1)当
时,用定义证明
是
上的严格增函数;
(2)若定义在
上的奇函数
满足当
时,
,求
在区间
上的反函数
;
(3)对于(2)中的
,若关于
的不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2476c8c0ae7946c94c3f2e401677e7f4.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e258ab9e600435b37465092243d99f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b2798c6a26d02c5d2c8b1355c8c30.png)
(2)若定义在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ead3fdcb8fe8f5eb3dbe7d96cabc28b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1938c093dd2fbcb752d0eb7a18d143b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/966d9dd819cba29980da3700422c2497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d1a94ea3c278c2197572cc1b7725b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1a1c92c42188e3b2cb800d1186eab12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
(3)对于(2)中的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/352fdc419e6b6b9eb5bfc24dde2eb965.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb87c830a03204a5b783ad4c2ba49c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2023-12-06更新
|
144次组卷
|
6卷引用:江苏省南京市第二十九中学2022-2023学年高一下学期2月期初考试数学试题
江苏省南京市第二十九中学2022-2023学年高一下学期2月期初考试数学试题上海市复旦大学附属中学2021-2022学年高一上学期期末数学试题江西省遂川中学2022-2023学年高一上学期期末考试数学试题(已下线)5.4 反函数-数学同步精品课堂(沪教版2020必修第一册)(已下线)单元高难问题03函数恒成立问题和存在性问题-【倍速学习法】(沪教版2020必修第一册)(已下线)专题16反函数-【倍速学习法】(沪教版2020必修第一册)
解题方法
2 . 已知函数
.
(1)求
的反函数
;
(2)若函数
,当
时,
,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9ed0bb77f64ec4df4a4f5dae56afbcc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32d6b59f4796a45963dea76b89c72bea.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e7c98d0986f51c040406c139354938a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac477594e609f621d5064581aebfde0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85cf5d3b1fa75e24552f90de2e3a325a.png)
您最近一年使用:0次
名校
解题方法
3 . 已知函数
.
(1)设
是
的反函数,当
时,解不等式
;
(2)若关于x的方程
的解集中恰好有一个元素,求实数a的值;
(3)设
,若
,对任意
,求a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ab5c53352f3eafd25b5dbf4ee5bbbd6.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a2a1822ac7392b61b2c0fffc1fbc05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf119627611a46c9bbc9f9dcaae9f51d.png)
(2)若关于x的方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56b91be0f393f09868cced8cace506c8.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16443926c89badae2361d1290e4781b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ef935409e7d226e0d959413a242a285.png)
您最近一年使用:0次
名校
4 . 已知函数
,
,
与
互为反函数.
(1)求
的解析式;
(2)若函数
在区间
内有最小值,求实数m的取值范围;
(3)若函数
,关于方程
有三个不同的实数解,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99eaeb2ab68a49074d623ffca072fed8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59eb51198230d07417b0807d6483855c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544f91d4fb22c571db9f8481b72a0419.png)
(2)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83b1e7c9c195e8d2c5f747a20038a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bef2b7bc9b4b7e3e77002bea81505aae.png)
(3)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a8f104c36a350e803917cbfb216cf2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc1836617c985de8b269a2c14203da0a.png)
您最近一年使用:0次
2022-01-02更新
|
1984次组卷
|
8卷引用:江苏省镇江市扬中市第二高级中学2022-2023学年高二上学期初摸底数学试题
江苏省镇江市扬中市第二高级中学2022-2023学年高二上学期初摸底数学试题四川省成都市蓉城名校联盟2021-2022学年高一上学期期末联考数学试题四川省遂宁中学校2021-2022学年高一下学期开学考试数学试题广东省深圳市高级中学(集团)2022-2023学年高一上学期期末考试数学试题江西省泰和中学2022-2023学年高一上学期期末数学试题(已下线)重难点03函数(15种解题模型与方法)(3)河南省郑州市为民高中2023-2024学年高一上学期11月月考数学试题(已下线)模块四专题4 大题分类练(对数函数及其应用)拔高提升练(人教A)
2021高一·全国·专题练习
解题方法
5 . 已知函数y=f(x)是函数y=
的反函数.
(1)求y=f(x)的解析式;
(2)若x∈(0,+∞),试分别写出使不等式:
①
;
②
成立的自变量x的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/082b3321f1d781d1ba481e520001ce56.png)
(1)求y=f(x)的解析式;
(2)若x∈(0,+∞),试分别写出使不等式:
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/087c0874a8f9289604c0278bb03e4eac.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ba3d6e2c588a9a3e345919f797d9e7b.png)
您最近一年使用:0次
2020高一·上海·专题练习
解题方法
6 . 已知函数
=
(x>1).
(1)求
的反函数
;
(2)判定
在其定义域内的单调性;
(3)若不等式(1-
)
>
(
-
)对
∈[
,
]恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e2bffe8821a4e9f0140ee04a8313b.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a2a1822ac7392b61b2c0fffc1fbc05.png)
(2)判定
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a2a1822ac7392b61b2c0fffc1fbc05.png)
(3)若不等式(1-
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f457e696b1504bfb73140699a8e18dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14a2a1822ac7392b61b2c0fffc1fbc05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f457e696b1504bfb73140699a8e18dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8d1ca7682da10dc7f36e858593d51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
2021高三·江苏·专题练习
7 . 设
,其中常数
.
(1)设
,
,求函数
(
)的反函数;
(2)求证:当且仅当
时,函数
为奇函数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa8240926fe03396a84d96165dd6aa58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10bbdef421c976962a270a2beabbad91.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964b2953a2d69ee37402d392481162bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02cab1add26335b3cb43d5b54c7c853.png)
(2)求证:当且仅当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51c530f4b7491b95acb8ce3eef9aa09d.png)
您最近一年使用:0次